118 research outputs found
Scattering of solitary waves in granular media
A detailed numerical study of the scattering of solitary waves by a barrier,
in a granular media with Hertzian contact, shows the existence of secondary
multipulse structures generated at the interface of two "sonic vacua", which
have a similar structure as the one previously found by Nesterenko and
coworkers.Comment: 4 pages, 9 figures (fig 5, replaced). Submitted to PR
Korn's second inequality and geometric rigidity with mixed growth conditions
Geometric rigidity states that a gradient field which is -close to the
set of proper rotations is necessarily -close to a fixed rotation, and is
one key estimate in nonlinear elasticity. In several applications, as for
example in the theory of plasticity, energy densities with mixed growth appear.
We show here that geometric rigidity holds also in and in
interpolation spaces. As a first step we prove the corresponding linear
inequality, which generalizes Korn's inequality to these spaces
DEVELOPMENT OF QGIS PLUGIN FOR URBAN ENERGY SIMULATION USING 3D CITY MODEL AT THE CITY DISTRICT LEVEL
In the context of climate change, the increasing demand for energy-efficient buildings and sustainable urban development has become a pressing issue due to the significant proportion of global energy consumption and carbon dioxide (CO2) emissions attributable to the building sector. This requires a concerted effort to reduce its environmental impact, and Geographic Information System (GIS) applications are vital tools for achieving this by optimizing heat supply, calculating costs, analyzing profitability, and balancing CO2 emissions. This study aims to address the challenge of achieving energy efficiency and reducing CO2 emissions in the building sector, specifically at the district level. To this end, the research objective is to develop a QGIS plugin that can simulate urban energy demand at the district level by integrating 2D data with CityGML files and connecting QGIS to SimStadt software via API to visualize the simulated urban energy results in 3D on the Web Globe. The proposed plugin leverages the open-source QGIS tool QField to capture building conditions and connect 2D and 3D data on urban energy simulation. Supplementary to this, this plugin provides up-to-date information on energy demand, consumption, CO2 emissions, building component conditions via updating related tables in the database. Decision-makers can use this comprehensive and user-friendly tool to understand and act on the results, ultimately leading to a CO2-neutral district by 2045. The development of the QGIS plugin represents a significant step towards sustainable urban development and climate change mitigation by utilizing GIS applications for optimizing energy demand and reducing CO2 emissions in the built environment
Translationally invariant nonlinear Schrodinger lattices
Persistence of stationary and traveling single-humped localized solutions in
the spatial discretizations of the nonlinear Schrodinger (NLS) equation is
addressed. The discrete NLS equation with the most general cubic polynomial
function is considered. Constraints on the nonlinear function are found from
the condition that the second-order difference equation for stationary
solutions can be reduced to the first-order difference map. The discrete NLS
equation with such an exceptional nonlinear function is shown to have a
conserved momentum but admits no standard Hamiltonian structure. It is proved
that the reduction to the first-order difference map gives a sufficient
condition for existence of translationally invariant single-humped stationary
solutions and a necessary condition for existence of single-humped traveling
solutions. Other constraints on the nonlinear function are found from the
condition that the differential advance-delay equation for traveling solutions
admits a reduction to an integrable normal form given by a third-order
differential equation. This reduction also gives a necessary condition for
existence of single-humped traveling solutions. The nonlinear function which
admits both reductions defines a two-parameter family of discrete NLS equations
which generalizes the integrable Ablowitz--Ladik lattice.Comment: 24 pages, 4 figure
Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations
In this paper we motivate, formulate and analyze the Multi-Configuration
Time-Dependent Hartree-Fock (MCTDHF) equations for molecular systems under
Coulomb interaction. They consist in approximating the N-particle Schrodinger
wavefunction by a (time-dependent) linear combination of (time-dependent)
Slater determinants. The equations of motion express as a system of ordinary
differential equations for the expansion coefficients coupled to nonlinear
Schrodinger-type equations for mono-electronic wavefunctions. The invertibility
of the one-body density matrix (full-rank hypothesis) plays a crucial role in
the analysis. Under the full-rank assumption a fiber bundle structure shows up
and produces unitary equivalence between convenient representations of the
equations. We discuss and establish existence and uniqueness of maximal
solutions to the Cauchy problem in the energy space as long as the density
matrix is not singular. A sufficient condition in terms of the energy of the
initial data ensuring the global-in-time invertibility is provided (first
result in this direction). Regularizing the density matrix breaks down energy
conservation, however a global well-posedness for this system in L^2 is
obtained with Strichartz estimates. Eventually solutions to this regularized
system are shown to converge to the original one on the time interval when the
density matrix is invertible.Comment: 48 pages, 1 figur
On the effect of interactions beyond nearest neighbours on non-convex lattice systems
We analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation
Orthogonality conditions and asymptotic stability in the Stefan problem with surface tension
We prove nonlinear asymptotic stability of steady spheres in the two-phase
Stefan problem with surface tension. Our method relies on the introduction of
appropriate orthogonality conditions in conjunction with a high-order energy
method.Comment: 25 pages, important references added, two remarks added, typos
correcte
A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry
We present here a review of the fundamental topics of Hartree-Fock theory in
Quantum Chemistry. From the molecular Hamiltonian, using and discussing the
Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock
equations for the electronic problem. Special emphasis is placed in the most
relevant mathematical aspects of the theoretical derivation of the final
equations, as well as in the results regarding the existence and uniqueness of
their solutions. All Hartree-Fock versions with different spin restrictions are
systematically extracted from the general case, thus providing a unifying
framework. Then, the discretization of the one-electron orbitals space is
reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition
of the basic underlying concepts related to the construction and selection of
Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we
close the review with a section in which the most relevant modern developments
(specially those related to the design of linear-scaling methods) are commented
and linked to the issues discussed. The whole work is intentionally
introductory and rather self-contained, so that it may be useful for non
experts that aim to use quantum chemical methods in interdisciplinary
applications. Moreover, much material that is found scattered in the literature
has been put together here to facilitate comprehension and to serve as a handy
reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and
subeqn package
International registry on the use of the CytoSorb® adsorber in ICU patients
INTRODUCTION: The aim of this clinical registry is to record the use of CytoSorb® adsorber device in critically ill patients under real-life conditions. METHODS: The registry records all relevant information in the course of product use, e. g., diagnosis, comorbidities, course of the condition, treatment, concomitant medication, clinical laboratory parameters, and outcome (ClinicalTrials.gov Identifier: NCT02312024). Primary endpoint is in-hospital mortality as compared to the mortality predicted by the APACHE II and SAPS II score, respectively. RESULTS: As of January 30, 2017, 130 centers from 22 countries were participating. Data available from the start of the registry on May 18, 2015 to November 24, 2016 (122 centers; 22 countries) were analyzed, of whom 20 centers from four countries provided data for a total of 198 patients (mean age 60.3 ± 15.1 years, 135 men [68.2%]). In all, 192 (97.0%) had 1 to 5 Cytosorb® adsorber applications. Sepsis was the most common indication for CytoSorb® treatment (135 patients). Mean APACHE II score in this group was 33.1 ± 8.4 [range 15-52] with a predicted risk of death of 78%, whereas the observed mortality was 65%. There were no significant decreases in the SOFA scores after treatment (17.2 ± 4.8 [3-24]). However interleukin-6 levels were markedly reduced after treatment (median 5000 pg/ml before and 289 pg/ml after treatment, respectively). CONCLUSIONS: This third interim report demonstrates the feasibility of the registry with excellent data quality and completeness from 20 study centers. The results must be interpreted with caution, since the numbers are still small; however the disease severity is remarkably high and suggests that adsorber treatment might be used as an ultimate treatment in life-threatening situations. There were no device-associated side effects
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